# Tag Info

44

In addition to the other answers, here is something for the intuition: $$V=RI$$ More "pressure" $V$ (more correctly: higher "pressure" difference from one side to the other) is required to keep the flow $I$ of charges constant when the flow is resisted by $R$. A thin wire has higher resistance than a thick wire, $R=\rho L/A$) analogous to a "bottleneck" ...

29

Nerd Sniping! The answer is $\frac{4}{\pi} - \frac{1}{2}$. Simple explanation: Successive Approximation! I'll start with the simplest case (see image below) and add more and more resistors to try and approximate an infinite grid of resistors. Mathematical derivation:

29

You're actually hitting on a very famous concept here that revolutionized physics!! Your understanding is almost wholly correct and your analogy is a good one - excellent reasoning - the only thing missing is radiation from the system. This latter lack is mostly irrelevant for the level of question you have been thinking about: but I'll address that below. ...

24

Ohm's law is generally NOT correct, it's called a law for historical reasons only!! It's a law in the same sense in which Hooke's law is a law... it holds only for certain systems under certain conditions, but it's widely known because it's simple and linear! It's not just superconductors, diodes are a neat everyday example of Ohm's law failing to hold. But ...

23

It's not true. To see this, you can try an experiment with some batteries and light bulbs. Hook up two bulbs of different wattages (that is, with different resistances) in parallel with a single battery: ------------------------------------------ | | | Battery Bulb 1 Bulb 2 | ...

23

You can use a high vertical tube to store water in it (fill it from the bottom by pushing the water in) How much water can you store? It obviously depends on the pressure you apply to push it in. If you push harder, there will be more water stored. The tube is characterized not the amount of water, but by how easy it is to store the water. Its "capacity" ...

22

First, Field strength. This calculation is strictly an electric potential calculation; radiation and induction are safely ignored at 50Hz.* For a 200kV transmission line 20m above ground, the max electric field at ground level is about 1.2 kV/m.** This number is reduced from the naive 200kV/20m=10 kV/m calculation by two effects: 1) The ~1/r variation ...

20

The identity $$V = K \frac{dV}{dt}$$ is only guaranteed with a constant $K$ if your assumptions actually hold. The first identity $V=RI$ only holds for a resistor, while the other holds for a capacitor. So in this sense, the letters $V,I$ in these equations mean something else. In one of them, it's the current through (or voltage on) a particular resistor, ...

17

$\def\vE{{\vec{E}}}$ $\def\vD{{\vec{D}}}$ $\def\vB{{\vec{B}}}$ $\def\vJ{{\vec{J}}}$ $\def\vr{{\vec{r}}}$ $\def\vA{{\vec{A}}}$ $\def\vH{{\vec{H}}}$ $\def\ddt{\frac{d}{dt}}$ $\def\rot{\operatorname{rot}}$ $\def\div{\operatorname{div}}$ $\def\grad{\operatorname{grad}}$ $\def\rmC{{\mathrm{C}}}$ $\def\rmM{{\mathrm{M}}}$ $\def\ph{{\varphi}}$ $\def\eps{{\varepsilon}... 17 Start with the initial diagram, but let's color code everything: Now move some wires around, without actually changing the connectivity: Finally, rotate the left and right blocks while again not changing the connectivity: 17 In a superconductor, the current can keep flowing "forever" since there is no resistance. But since conductors have inductance (in fact, superconductors are used most often to create magnets like for an MRI scanner), applying a voltage would not (immediately) cause an infinite current to flow. It is instructive to see how an MRI magnet is "ramped" (turned ... 17 Capacitors and inductors are images of one another under the self-inverse mapping that transforms a linear electrical network to its dual network. The network duality transformation maps the network's graph to its topological dual graph,then all the impedances (either as lone-frequency complex scalars or as Laplace transfer functions) in the dual graph ... 16 Yes Sam, there definitely is electric field reshaping in the wire. Strangely, it is not talked about in hardly any physics texts, but there are surface charge accumulations along the wire which maintain the electric field in the direction of the wire. (Note: it is a surface charge distribution since any extra charge on a conductor will reside on the surface.)... 16 Outside a current carrying conductor, there is, in fact, an electric field. This is discussed for example, in "Surface charges on circuit wires and resistors play three roles" by J. D. Jackson, in American Journal of Physics -- July 1996 -- Volume 64, Issue 7, pp. 855 . To quote Norris W. Preyer quoting Jackson, "Jackson describes the three roles of surface ... 16 where does that electricity go? The photons from the sun have energy and momentum, but not "electricity". Essentially, a photon (solar or otherwise) striking the solar panel can create an electron-hole pair (EHP) and, if the EHP is within or near the depletion zone, the pair will be separated by the built-in electric field. This results in a separation ... 16 The physical 'meaning' of the imaginary part of the impedance is that it represents the energy storage part of the circuit element. To see this, let the sinusoidal current$i = I\cos(\omega t)$be the current through a series RL circuit. The voltage across the combination is $$v = Ri + L\frac{di}{dt} = RI\cos(\omega t) - \omega LI\sin(\omega t)$$ The ... 15 Yes, it is possible. For example Kevin Brown did here and here including this table. so for the xkcd problem the answer is$-\frac{1}{2}+\frac{4}{\pi} \approx 0.773\$.

15

Ohm's law works for ordinary conductors for a reason: the particles carrying the current (usually, but not always electrons) scatter incoherently and inelastically from features of the conductor. In the case of an electron current, at low temperature this scattering is caused by impurities in the conductor; at high temperatures, the dominant source of ...

15

For static charges, the relationship is V (voltage) = Q (charge) / C (capacitance). Capacitance is a function of the shape, size and distance between objects, which are all continuous values. (Well, I suppose you could argue that shape and size are quantized to the atomic spacing of the object's material, but you can't say the same thing for distance.) So ...

14

Sine and cosine waves are, physically, the most common. They are definitely the best description to what comes out of a wall socket, not because we like them mathematically, but because it's what comes out; electromotive force is generated in the power plant as a sinusoidal pattern with frequency 50/60 Hz. In the usual kind of generator, this is because in ...

14

Another term is thermal resistance, This is incorrect. Thermal resistance is something that prevents heat flow. It is an entirely separate concept from electrical resistance. How is contact resistance explained? To obtain very low resistance in a material like most metals, the electrons must be delocalized from the individual atoms, and free flow ...

13

Most probably yes; wireless devices are not grounded, so they are not lighting rods of any kind as it is frequently assumed. There are some theories that cell phones somehow attracts lightnings by the field they produce, but the theory behind is weak. Experimental evaluation is very hard, since lightning hits are quite rare, such events are guided by ...

13

AC or DC, you only get electrocuted if current passes through your body. (Current passing through any part of your body can be dangerous, and possibly cause an electrical burn, but current passing across your heart is the one that's really dangerous.) Touching just one wire at a time gives the current nowhere much to go. You are right to think that some ...

12

Although the question is not clear, my guess is that you are confused with the flow of current and mean position of electrons. In case of DC, we have a continuous flow of charge from one point to another point in the conductor, any electron completes a cycle of circuit. In case of AC, there is no net displacement of charge and this may lead one in ...

12

Alfred got in before me, but I have a diagram! I've marked all continuous bits of wire in the same colour, and marked the corresponding colours on the ends of the resistors. A quick redraw later and I get: which is a lot simpler!

11

First, your camera is not designed to work with batteries below a certain voltage. When it detects an excessively low battery voltage it turns itself off. That circuit stays in the "off" state until voltage is completely removed from the circuit. When you operate your camera, the current required by your camera varies according to what you do with it. So ...

11

EDIT: Put simply, potential difference is the work done by electrostatic force on a unit charge, while EMF is the work done by anything other than electrostatic force on a unit charge. I don't like the term "voltage". It seems to mean anything measured in volts. I'd rather say electric potential and electromotive force. And the two are fundamentally ...

11

In ideal circuit theory, the parallel connection of two voltage sources results in an inconsistent equation, e.g., a 3V and 2V source connected in parallel, by KVL, gives the equation: 3 = 2. In the real world, batteries are not ideal voltage sources; batteries can supply a limited current and the voltage across the battery does, in fact, depend on the ...

11

Why are wires in simple circuits approximated as equipotentials? Because one of the three assumptions of circuit theory is: All electrical effects happen instantaneously throughout a circuit. If the circuit is small enough compared to the wave length of the signals applied, all electric signals travel through it so quickly, that we can assume that they ...

11

Actually, induction works, although it is often used a bit differently than you described. You can place a warm superconductor loop into a normal coil. As you switch the coil on, there will be some current inside the superconductor, but since it is not cold yet, this current quickly dies down. Then you cool the superconductor below its critical temperature. ...

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